The invention relates to a clamp device for axially clamping a tool, particularly a disc, and which comprises a clamp nut and a clamp located between the disc and the clamp nut and connected with the clamp nut with a possibility of an axial movement relative thereto. Clamp devices of this kind are mainly suitable for portable hand machine tools and in this connection particularly grinding machines. A clamp device of the kind mentioned is known (German Patent Specification No. 3,012,836), in which the clamp disc consists of a member which has an approximately hat-shaped cross-section and which is supported axially against the flange of the clamp nut by a coil spring. When the clamp nut is screwed on and tightened, this clamp disc is pressed axially against the tool by the axially compressed spring and thus the tool is tightened against the flange on the spindle side, while the, end face of a cylindrical extension of the clamp nut abuts directly against a facing axial side of the flange on the spindle side and, when the clamp nut is further tightened the flange on the spindle side is tightened, together with the clamp nut, possibly until the rear flange abuts axially against the spindle shoulder surface forming the supporting member. It is thereby intended, in the case of an angle grinder, to enable the grinding wheel to be clamped with a predetermined contact pressure and to ensure that this contact pressure is maintained. This clamp device is also intended to allow rapid and, simple changing of the grinding wheel and at the same time, to avoid overloading of the hand machine tool, particularly of the angle grinder. If in fact the torque acting on the grinding wheel is too high, the grinding wheel stops whereas the rear flange and the clamp nut together with the clamp disc make a relative movement in relation to it. This clamp device counteracts the effect of the further spontaneous tightening of the clamp nut during operation, which would otherwise make it considerably more difficult to loosen the clamp nut for the purpose of changing the grinding wheel. Nevertheless, the clamp nut can here be unscrewed only with aid of a special auxiliary tool, while, depending on the construction of the machine, the spindle has to be securely held correspondingly fast with a second auxiliary tool, for example a spanner.